Thanks Essexboy. I ran FRST using the fixlist you sent me. The fixlog is attached.
Several attempts to download the ADW cleaner were unsuccessful. I proceeded to again try reinstalling Avast, but after uninstalling it I found a way to download the cleaner and ran it even though Avast was no longer on the computer. I did not find the ADW log file you mentioned at the exact location you gave or with the exact name but I found two log files in a similar location with similar names and I'm attaching them.
As I mentioned in my first posting to this forum, I had already uninstalled and reinstalled Avast before posting. I removed it as thoroughly as I could, but after the new installation the background program was still stopping every ~20 minutes. Today I again uninstalled the program, and then removed all the Avast folders I could find, and did a registry cleaning. Then I downloaded Avast from your site and reinstalled it (after running the ADW cleaner, as mentioned). I'm afraid the Avast service still stops about every 20 minutes.